Abstract

We work out the decoupling problem and hydrodynamic analysis for the sound mode in charged AdS black hole and calculate the sound velocity, the charge susceptibility and the electrical conductivity. We find that Einstein relation among the conductivity, the diffusion constant and the susceptibility holds exactly.

Here, we explore a version of black hole complementarity, where an approximate semiclassical effective field theory for interior infalling degrees of freedom emerges holo-graphically from an exact evolution of exterior degrees of freedom. The infalling degrees of freedom have a complementary description in terms of outgoing Hawking radiation and must eventually decohere with respect to the exterior Hamiltonian, leading to a breakdown of the semiclassical description for an infaller. Trace distance is used to quantify the difference between the complementary time evolutions, and to define a decoherence time. We propose a dictionary where the evolution with respect to the bulkmore » effective Hamiltonian corresponds to mean field evolution in the holographic theory. In a particular model for the holographic theory, which exhibits fast scrambling, the decoherence time coincides with the scrambling time. The results support the hypothesis that decoherence of the infalling holographic state and disruptive bulk effects near the curvature singularity are comple-mentary descriptions of the same physics, which is an important step toward resolving the black hole information paradox.« less

To gain insight into how bulk locality emerges from the holographic conformal field theory (CFT), we reformulate the bulk-to-boundary map in as local a way as possible. In previous work, we carried out this program for Lorentzian anti-de Sitter (AdS), and showed the support on the boundary could always be reduced to a compact region spacelike separated from the bulk point. In the present work the idea is extended to a complexified boundary, where spatial coordinates are continued to imaginary values. This continuation enables us to represent a local bulk operator as a CFT operator with support on a finitemore » disc on the complexified boundary. We treat general AdS in Poincare coordinates and AdS{sub 3} in Rindler coordinates. We represent bulk operators inside the horizon of a Banados-Teitelboim-Zanelli (BTZ) black hole and we verify that the correct bulk two-point functions are reproduced, including the divergence when one point hits the BTZ singularity. We comment on the holographic description of black holes formed by collapse and discuss locality and holographic entropy counting at finite N.« less

It is shown that the hidden conformal symmetry, namely SO(2,2){approx}SL(2,R){sub L}xSL(2,R){sub R} symmetry, of the nonextremal dyonic Reissner-Nordstroem black hole can be probed by a charged massless scalar field at low frequencies. The existence of such hidden conformal symmetry suggests that the field theory holographically dual to the four-dimensional Reissner-Nordstroem black hole indeed should be a two-dimensional conformal field theory (CFT). Although the associated AdS{sub 3} structure does not explicitly appear in the near horizon geometry, the primary parameters of the dual CFT{sub 2} can be exactly obtained without the necessity of embedding the four-dimensional Reissner-Nordstroem black hole into five-dimensionalmore » spacetime. The duality is further supported by comparing the absorption cross sections and real-time correlators obtained from both the CFT and the gravity sides.« less

An analysis is made of the manner in which the process of primordial black-hole formation and the subsequent accretion of gas depend on the equation of state. On the assumption that the process is spherically symmetric, the problem is solved numerically.